diff --git a/lib/media/media_source_engine.js b/lib/media/media_source_engine.js
index f7a53d8989..09665609a7 100644
--- a/lib/media/media_source_engine.js
+++ b/lib/media/media_source_engine.js
@@ -1424,7 +1424,7 @@ shaka.media.MediaSourceEngine = class {
     const ContentType = shaka.util.ManifestParserUtils.ContentType;
     if (contentType == ContentType.TEXT) {
       await this.textEngine_.remove(startTime, endTime);
-    } else {
+    } else if (endTime > startTime) {
       await this.enqueueOperation_(
           contentType,
           () => this.remove_(contentType, startTime, endTime),
diff --git a/lib/media/streaming_engine.js b/lib/media/streaming_engine.js
index c09d9396a9..49d5ff933c 100644
--- a/lib/media/streaming_engine.js
+++ b/lib/media/streaming_engine.js
@@ -2430,15 +2430,26 @@ shaka.media.StreamingEngine = class {
     }
     const bufferedBehind = presentationTime - startTime;
 
-    const overflow = bufferedBehind - bufferBehind;
+    const evictionGoal = this.config_.evictionGoal;
+
+    const seekRangeStart =
+        this.manifest_.presentationTimeline.getSeekRangeStart();
+    const seekRangeEnd =
+        this.manifest_.presentationTimeline.getSeekRangeEnd();
+
+    let overflow = bufferedBehind - bufferBehind;
+    if (seekRangeEnd - seekRangeStart > evictionGoal) {
+      overflow = Math.max(bufferedBehind - bufferBehind,
+          seekRangeStart - evictionGoal - startTime);
+    }
     // See: https://github.com/shaka-project/shaka-player/issues/6240
-    if (overflow <= this.config_.evictionGoal) {
+    if (overflow <= evictionGoal) {
       shaka.log.v2(logPrefix,
           'buffer behind okay:',
           'presentationTime=' + presentationTime,
           'bufferedBehind=' + bufferedBehind,
           'bufferBehind=' + bufferBehind,
-          'evictionGoal=' + this.config_.evictionGoal,
+          'evictionGoal=' + evictionGoal,
           'underflow=' + Math.abs(overflow));
       return;
     }
@@ -2448,7 +2459,7 @@ shaka.media.StreamingEngine = class {
         'presentationTime=' + presentationTime,
         'bufferedBehind=' + bufferedBehind,
         'bufferBehind=' + bufferBehind,
-        'evictionGoal=' + this.config_.evictionGoal,
+        'evictionGoal=' + evictionGoal,
         'overflow=' + overflow);
 
     await this.playerInterface_.mediaSourceEngine.remove(mediaState.type,
diff --git a/test/media/streaming_engine_unit.js b/test/media/streaming_engine_unit.js
index 296988ea11..0f979e9c48 100644
--- a/test/media/streaming_engine_unit.js
+++ b/test/media/streaming_engine_unit.js
@@ -456,6 +456,9 @@ describe('StreamingEngine', () => {
       config.bufferingGoal = 5;
       config.bufferBehind = Infinity;
       config.maxDisabledTime = 0; // Do not disable stream by default
+      // We don't want to evict segments in tests where there is no need to
+      // test them.
+      config.evictionGoal = 30;
     }
 
     if (defaultConfig.segmentPrefetchLimit == config.segmentPrefetchLimit) {